Interpreting Data (DP IB Applications & Interpretation (AI)): Revision Note

Interpreting data

How do I interpret statistical measures?

• The mode is useful for qualitative data

  • It is not as useful for quantitative data as there is not always a unique mode

• The mean includes all values

  • It is affected by outliers

  • A smaller/larger mean is preferable depending on the scenario

    • A smaller mean time for completing a puzzle is better

    • A bigger mean score on a test is better

• The median is not affected by outliers

  • The size of the biggest and smallest values is not used when finding the median

• The range gives the full spread of the all of the data

  • It is affected by outliers

• The interquartile range gives the spread of the middle 50% about the median and is not affected by outliers

  • It does not use the biggest and smallest values

  • A bigger IQR means the data is more spread out about the median

  • A smaller IQR means the data is more centred about the median

• The standard deviation and variance use all the values to give a measure of the average spread of the data about the mean

  • They are affected by outliers

  • A bigger standard deviation means the data is more spread out about the mean

  • A smaller standard deviation means the data is more centred about the mean

How do I choose which diagram to use to represent data?

• Box plots

  • Can be used with ungrouped univariate data

  • Shows the range, interquartile range and quartiles clearly

  • Very useful for comparing data patterns quickly

• Cumulative frequency graphs

  • Can be used with continuous grouped univariate data

  • Shows the running total of the frequencies that fall below the upper bound of each class

• Histograms

  • Can be used with continuous grouped univariate data

  • Used with equal class intervals

  • Shows the frequencies of the group

• Scatter diagrams

  • Can be used with ungrouped bivariate data

  • Shows the graphical relationship between the variables

How do I compare two or more data sets?

• Compare a measure of central tendency

  • If the data contains outliers - use the median

  • If the data is roughly symmetrical – use the mean

• Compare a measure of dispersion

  • If the data contains outliers - use the interquartile range

  • If the data is roughly symmetrical – use the standard deviation

• Consider whether it is better to have a smaller or bigger average

  • This will depend on the context

    • A smaller average time for completing a puzzle is better

    • A bigger average score on a test is better

• Consider whether it is better to have a smaller or bigger spread

  • Usually a smaller spread means it is more consistent

• Always relate the comparisons to the context and consider reasons

  • Consider the sampling technique and the data collection method